New Ab Initio Nuclear Structure Theory: Progress and...
Transcript of New Ab Initio Nuclear Structure Theory: Progress and...
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Ab Initio Nuclear Structure Theory:
Progress and Prospects
James P. Vary, Iowa State University
Nuclei in the Laboratoryand in the Cosmos
Erice, Italy, September 20, 2014
FRIB
HIRFL
BRIF
RISP
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Predic've nuclear theory with quan'fied uncertain'es for
prac'cal and fundamental physics
Effec've Field Theory (pionless, pionful,
deltaful,…)
Ab-‐ini'o many-‐body theory: structure & reac'ons
Computa'onal Science: Fully exploit disrup've
technologies
Applied Mathema'cs: New/improved algorithms
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The Nuclear Many-Body Problem The many-body Schroedinger equation for bound states consists
of 2( ) coupled second-order differential equations in 3A coordinates using strong (NN & NNN) and electromagnetic interactions.
Successful ab initio quantum many-body approaches (A > 6)
Stochastic approach in coordinate space Greens Function Monte Carlo (GFMC)
Hamiltonian matrix in basis function space No Core Configuration Interaction (NCSM/NCFC)
Cluster hierarchy in basis function space Coupled Cluster (CC)
Lattice Nuclear Chiral EFT, MB Greens Function, MB Perturbation Theory, . . . approaches
Comments All work to preserve and exploit symmetries
Extensions of each to scattering/reactions are well-underway They have different advantages and limitations
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AZ
Meson Exchg interactions
Chiral EFT interactions
Featured results here
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• Adopt realistic NN (and NNN) interaction(s) & renormalize as needed - retain induced many-body interactions: Chiral EFT interactions and JISP16
• Adopt the 3-D Harmonic Oscillator (HO) for the single-nucleon basis states, α, β,… • Evaluate the nuclear Hamiltonian, H, in basis space of HO (Slater) determinants
(manages the bookkeepping of anti-symmetrization) • Diagonalize this sparse many-body H in its “m-scheme” basis where [α =(n,l,j,mj,τz)]
• Evaluate observables and compare with experiment
Comments • Straightforward but computationally demanding => new algorithms/computers • Requires convergence assessments and extrapolation tools • Achievable for nuclei up to A=16 (40) today with largest computers available
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Φn = [aα+ • • • aς
+]n 0
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n = 1,2,...,1010 or more!
No Core Shell Model A large sparse matrix eigenvalue problem
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H = Trel +VNN +V3N + • • •H Ψi = Ei Ψi
Ψi = Ani
n= 0
∞
∑ ΦnDiagonalize Φm H Φn{ }
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K=1/2 bands include Coriolis decoupling parameter:
Both natural and unnatural parity bands iden'fied Employed JISP16 interac'on; Nmax = 10 -‐ 7
K=1/2
K=1/2
K=3/2
K=3/2
K=1/2
K=1/2
Black line: Yrast band in collec've model fit Red line: excited band in collec've model fit
Physics Le]ers B 719, 179 (2013)
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M.A. Caprio, P. Maris and J.P. Vary, Physics Le]ers B 719, 179 (2013)
Note: Although Q, B(E2) are slowly converging, the ra'os within a rota'onal band appear remarkably stable
Next challenge: Inves'gate same phenomena with Chiral EFT interac'ons
Proton
Neutron
Collec've model:
Black line: Yrast band in collec've model fit Red line: excited band in collec've model fit
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9Be Translationally invariant gs density Full 3D densities: rotate around the vertical axis
Total density Proton-Neutron density
Shows that one neutron provides a “ring” cloud around two alpha clusters binding them together
C. Cockrell, J.P. Vary, P. Maris, Phys. Rev. C 86, 034325 (2012); arXiv:1201.0724; C. Cockrell, PhD, Iowa State University
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NN 3N 4N
long (2π) intermediate (π) short-range
c1, c3, c4 terms cD term cE term
1.5
large uncertainties in coupling constants at present:
Chiral EFT for nuclear forces, leading order 3N forces
lead to theoretical uncertainties inmany-body observables
use chiral interactions as input for RG evolution
NN 3N 4N
Adapted from Kai Hebeler, ECT* workshop May 2014
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H
P
Q
P
Q
Nmax
• n-body cluster approximation, 2≤n≤A • H(n)eff n-body operator • Two ways of convergence:
– For P → 1 H(n)eff → H – For n → A and fixed P: H(n)eff → Heff
Heff 0
0 QXHX-1Q
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H : E1, E2, E3,…EdP ,…E∞
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Heff : E1, E2, E3,…EdP
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QXHX−1P = 0
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Heff = PXHX−1P
X = − −+exp[ arctan ( )]h ω ωunitary
model space dimension
Effective Hamiltonian in the NCSM Okubo-Lee-Suzuki renormalization scheme
Adapted from Petr Navratil
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Both OLS and SRG derivations of Heff will be used in applications here
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Controlling the center-of-mass (cm) motion in order to preserve Galilean invariance
Add a Lagrange multiplier term acting on the cm alone so as not to interfere with the internal motion dynamics
H = Heff Nmax ,!!( )+"Hcm
Hcm =P2
2MA+ 1
2MA!
2R2
" "10 suffices
Low-lying “physical” spectrum
Approx. copy of low-lying spectrum
!!"Along with the Nmax truncation in the HO basis, the Lagrange multiplier term guarantees that all low-lying solutions have eigenfunctions that factorize into a 0s HO wavefunction for the cm times a translationaly invariant wavefunction.
Heff Nmax ,Ω( )≡ P[Trel +Va Nmax ,Ω( )]P
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ab initio No Core
Shell Model “NCSM”
No Core Full Config
NCFC
NCSM- Reson’g Grp
Method & NCSM-
Contin’m
SU(3)-NCSM
Basis Light Front Quant’zn
J-matrix Scat’g phase
shifts
Structure
Reactions Effective Field
Theory - ext’l field
Monte Carlo
NCSM
Importance Truncated
NCSM
NCSM with Core
Extensions of the ab initio NCSM
Gamow- NCSM &
Density Matrix Renormaliz’n
Group
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P. Maris, J. P. Vary and P. Navratil, Phys. Rev. C87, 014327 (2013); arXiv 1205.5686
Note additional predicted states! Shown as dashed lines
CD= -0.2
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J. Phys. Conf. Ser. 454, 012063 (2013)
SRG Renormalization scale invariance, convergence & agreement with experiment
8Be
λ=2.0 fm-1 λ=2.0 fm-1 λ=2.24 fm-1 λ=1.88 fm-1
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0! 0
2! 0
0! 0
1! 0
4! 01! 12! 02! 1
0! 1
0! 0
2 4 6 8 Exp.Nmax
0
2
4
6
8
10
12
14
16
18
20
.
Ex
[MeV
]
0! 0
2! 0
0! 0
1! 0
4! 01! 12! 02! 1
0! 1
0! 0
2 4 6 8 Exp.Nmax
0
2
4
6
8
10
12
14
16
18
20
.
Ex
[MeV
]
NCSM excita'on spectra for 12C with chiral NN(N3LO) + 3N(N2LO) interac'on
SRG evolu'on scale (in fm4) dependence
0.0625 0.08
0.04
HO frequency (in MeV) dependence
P. Maris, J.P. Vary, A. Calci, J. Langhammer, S. Binder and R. Roth, arXiv 1405.1331;to appear in PRC
20
16
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0! 0
2! 0
0! 0
1! 0
4! 0
1! 12! 0
2! 1
0! 0
4 6 8 10 Exp.Nmax
0
2
4
6
8
10
12
14
16
.
Ex
[MeV
]
3! 0
1! 0
2! 0
!2! 0"4! 0
3 5 7 9 Exp.Nmax
0
1
2
3
4
.
E−
E(3−
0)
[MeV
]
P. Maris, J.P. Vary, A. Calci, J. Langhammer, S. Binder and R. Roth, arXiv 1405.1331;to appear in PRC
Convergence rates of excita'on spectra for SRG evolved chiral NN(N3LO) + 3N(N2LO)
α = 0.0625 fm4
λ = 2.0 fm−1
!Ω = 20 MeVIT-‐NCSM
NCSM
IT-‐NCSM
NCSM
Boxes indicate threshold-‐extrapola'on uncertain'es for IT-‐NCSM
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JJJ
J
J
JJ
J
J
BBB
BB
B
B
B
B
HHH
HH
H
H
H
H
8
10
12
14
16
18
20
0 2 4 6 8
E ex(
3-) (
MeV
)
12C
Experiment
16
20
24
(MeV) !Ω
(0,1) (2,3) (4,5) (6,7) (8,9)(Nmax,Nmax+1)
α fm4( )0.080.06250.04
Convergence rates of selected observables for SRG evolved chiral NN(N3LO) + 3N(N2LO)
P. Maris, J.P. Vary, A. Calci, J. Langhammer, S. Binder and R. Roth, arXiv 1405.1331;to appear in PRC
JJ
JJ
JJJ
JJ
J
J
J
BB
BB
BBB
B
B
B
B
B
HHHH
HHHH
H
HH
H
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 2 4 6 8 10
B(M
1) (1
+ ,1)
to (0
+ ,0)
g.s
.
Nmax
Experiment
20
24
20
16
!Ω 12C(MeV)
16
24
α fm4( )0.040.06250.08
(µN2)
JJJ
JJ
JJ
J
J
J
J
J
BBB
B
BB
BB
B
B
B
B
HHH
H
HH
HH H
HH
H
0
1
2
3
4
5
6
7
8
9
0 2 4 6 8 10
B(E2
) (2+
,0) t
o (0
+ ,0)
g.s
. (e2
fm4 )
Nmax
Experiment
12C
16
20
24
!Ω (MeV)
α fm4( )0.080.06250.04
JJJJ
JJ
JJ J
J
J
J
BBBB
BB
BB
B
B
B
B
HHHH
HHH
H
H
H
H
H
1.9
2
2.1
2.2
2.3
2.4
0 2 4 6 8 10
Poin
t Pro
ton
RM
S R
adiu
s (fm
)
Nmax
Experiment
12C
α fm4( )0.080.06250.04
(MeV) !Ω
16
20
24
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Next Genera'on Ab Ini'o Structure Applica'ons – Aim for Precision
Electroweak processes Beyond the Standard Model tests (e.g. CKM unitarity => vud determina'on)
Neutrinoful and neutrinoless double beta-‐decay ?
Each puts major demands on theory, algorithms and computa'onal resources Growing demands => larger collabora'ng teams, growing computa'onal resources,
Increase in the mul'-‐disciplinary character, . . .
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Ground state magnetic moments with JISP16Maris, Vary, IJMPE, in press
µ =1
J + 1
(
⟨J · Lp⟩+ 5.586⟨J · Sp⟩ − 3.826⟨J · Sn⟩)
µ0
2 4 6 8 10 12 14 16A
-2
-1
0
1
2
3m
agne
tic m
omen
t (µ 0
)
exptJISP16
2H 6Li
8Li
8B
7Li
7Be9Be
9B9Li
9C
10B
11B
11C
11Be
15N
15O14N
13B
13O
13N
13C
?
?
12B
12N
3H
3He
Good agreement with data,given that we do not have any meson-exchange currents
SciDAC NUCLEI workshop, June 2013, Bloomington, IN – p. 13/37Pieter Maris
P. Maris and J.P. Vary, Int. J. Mod. Phys. E 22, 1330016 (2013)
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M1, E2, F, GT transitionsNO EFFECTIVE CHARGES!
E2 = eP
k12
ˆ
r2kY2(r̂k)˜
(1 + τkz)
M1 = µNP
k[(Lk + gpSk)(1 + τkz)/2
+ gnSk (1 − τkz)/2]
F =P
kτk± ; GT =P
kσkτk±
Pervin, Pieper & Wiringa, PRC 76, 064319 (2007)
Marcucci, Pervin, et al., PRC 78, 065501 (2008)
Cohen-KurathNCSMGFMC(IA)GFMC(MEC)Experiment 0 1 2 3
Ratio to experiment
6He(2+;0→0+;0) B(E2)
6Li(3+;0→1+;0) B(E2)
6Li(0+;1→1+;0) B(M1)
7Li(1/2-→3/2-) B(E2)
7Li(1/2-→3/2-) B(M1)
7Li(7/2-→3/2-) B(E2)
7Be(1/2-→3/2-) B(M1)
6He(0+)→6Li(1+) B(GT)
7Be(3/2-)→7Li(3/2-) B(GT)
7Be(3/2-)→7Li(1/2-) B(GT)
7Be(3/2-) Branching ratio
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Origin of the anomalously long life-time of 14C
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
GT
mat
rix e
lem
ent
no 3NF forceswith 3NF forces (cD= -0.2)with 3NF forces (cD= -2.0)
s p sd pf sdg pfh sdgi pfhj sdgik pfhjl
shell
-0.10
0.10.20.3
0.2924
near-completecancellationsbetweendominantcontributionswithin p-shell
very sensitiveto details
Maris, Vary, Navratil,
Ormand, Nam, Dean,
PRL106, 202502 (2011)
INT workshop on double beta decay, Aug. 2013, Seattle, WA – p. 32/35
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Impact Objec,ves • Predict proper'es of neutron-‐rich systems which relate
to exo'c nuclei and nuclear astrophysics • Determine how well high-‐precision phenomenological
strong interac'ons compare with effec've field theory based on QCD
• Produce accurate predic'ons with quan'fied uncertain'es
! Improve nuclear energy density func'onals used in extensive applica'ons such as fission calcula'ons
! Demonstrate the predic've power of ab ini,o nuclear theory for exo'c nuclei with quan'fied uncertain'es
! Guide future experiments at DOE-‐sponsored rare isotope produc'on facili'es
1. Demonstrates predic've power of ab ini,o nuclear structure theory.
2. Provides results for next genera'on nuclear energy density func'onals
3. Leads to improved predic'ons for astrophysical reac'ons
4. Demonstrates that the role of three-‐nucleon (3N) interac'ons in extreme neutron systems is significantly weaker than predicted from high-‐precision phenomemological interac'ons
Accomplishments
Ab ini&o Extreme Neutron Ma2er
Comparison of ground state energies of systems with N neutrons trapped in a harmonic oscillator with strength 10 MeV. Solid red diamonds and blue dots signify new results with two-‐nucleon (NN) plus three-‐nucleon (3N) interac,ons derived from chiral effec,ve field theory related to QCD. Inset displays the ra,o of NN+3N to NN alone for the different interac,ons. Note that with increasing N, the chiral predic,ons lie between results from different high-‐precision phenomenological interac,ons, i.e. between AV8’+UIX and AV8’+IL7.
References: P. Maris, J.P. Vary, S. Gandolfi, J. Carlson, S.C. Pieper, Phys. Rev. C87, 054318 (2013); H. Po]er, S. Fischer, P. Maris, J.P. Vary, S. Binder, A. Calci, J. Langhammer and R.Roth, arXiv:1406.1160; Contact: [email protected]
E tot
/(10
MeV⇥
N4/3)
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
N4 6 8 10 12 14 16 18 20 28 40 50
NN+3N-ind. ( NCSM)NN+3N-full ( NCSM)NN+3N-ind. (⇤CCSD(T))NN+3N-full (⇤CCSD(T))AV8’ (QMC)AV8’+UIX (QMC)AV8’+IL7 (QMC)
(NN
+3N
)/N
N
0.96
0.98
1.00
1.02
4 8 12 16
ChiralUIX
IL7
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Summary: Observables in light nuclei known to be sensi've to 3NFs Binding energies (through Oxygen)and subshell closures (through Calcium) Spectral proper'es having spin-‐orbit sensi'vity GS quadrupole moment of 6Li M1, E2, F, GT transi'ons Ra'o of B(E2)’s [GS -‐> 11+ over GS -‐> 12+] in 10B 10B ground state spin 14C anomalous half-‐life Other: Elas'c magne'c form factor of 17O (M5 region)
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Established challenges – possible roles for improved 3NFs Gaps between natural & unnatural parity spectra The energy of J = 1+, T=0 state in 12C Two low-‐lying 2+ states in 10Be with radically different B(E2)’s Level crossing of J = 5/2 and J = 1/2 states in 9Be Spectra of 14N Overbinding of Ca isotopes and above RMS radii too small in ~all nuclei above 4He Magne'c FF of 17O – in the M3 suppression region Extra GT transi'ons (intruders, clusters, . . .) in p-‐shell nuclei (e.g. A = 14 PRL) How JISP16 and NNLO_opt do a ~reasonable job simula'ng 3NF effects
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Future Prospects Extend the Precision and Reach of Ab Ini'o Applica'ons by Improved:
chiral interac'ons, EW currents, . .
basis spaces Renormaliza'on theory Extrapola'on theory
Op'mize our u'liza'on of available algorithms and computa'onal resources => intense theore'cal developments
=> increase in mul'-‐disciplinary collabora'ons
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Low Energy Nuclear Physics International Collaboration
E. Epelbaum, H. Krebs
A. Nogga
P. Maris, J. Vary
J. Golak, R. Skibinski, K. Tolponicki, H. Witala
S. Binder, A. Calci, K. Hebeler,J. Langhammer, R. Roth
R. Furnstahl
H. Kamada
Calculation of three-body forces at N3LO
Goal
Calculate matrix elements of 3NF in a partial-
wave decomposed form which is suitable for
different few- and many-body frameworks
Challenge
Due to the large number of matrix elements,
the calculation is extremely expensive.
Strategy
Develop an efficient code which allows to
treat arbitrary local 3N interactions.
(Krebs and Hebeler)
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H
PHeffP
PHeffQ = 0
QHeffP = 0
QHeffQ
P Q
P
Q
Nmax
The “double Lee-Suzuki transform” for valence Heff
P’H’EFFP’ Nmax=0
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Aim: Regain valence-core separation but retain full ab initio NCSM
=> “Double OLS” Approach
Now extend to s-d shell the successful p-shell applications
p-shell application:
A. F. Lisetskiy, B. R. Barrett,
M. K. G. Kruse, P. Navratil,
I. Stetcu, J. P. Vary,
Phys. Rev. C. 78, 044302 (2008); arXiv:0808.2187
Preliminary Results
Excellent
Spectral
agreement!
Total Binding
Energies!
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(26 of 37)! International Conference on Nuclear Theory in the Superconducting Era, Iowa State, 12-17 May 2013 !Unraveling Mysteries of
the Strong Interaction !
Choose Three Slices (ancient but current)!Hoyle State Example !
Main contribution to ground state rotational band (0g.s.+, 21+, 41+)
(0 4) Bandhead (Oblate)
0p-0h!
Main contribution to Hoyle state (02+)
4p-4h!
(12 0) Bandhead (More Prolate)
(6 2) Bandhead (Prolate)
Main contribution to the 03+
2p-2h!
‘Back to the Future’ !– déjà vu –!
Engeland & Ellis ‘67s
J.P. Draayer, et al
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" Hardware advances: Moore’s Law " Theory/Algorithms/Sowware advances: Doubles Moore’s Law
Discovery poten'al increases geometrically
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B
B
B
B
B
J
J
J
J
J
HHHH
H
1.97
1.975
1.98
1.985
1.99
1.995
2
2.005
2.01
0 0.02 0.04 0.06 0.08 0.1
Mass/mf X
X
X
µ /mf
11S0
13S1
23P2
2nd degree polynomial fitsAll points are Nmax -> inf at largest K availableMax K = 65 for mu = 0.02, 0.04 & 45 for mu > 0.04
α = 0.3b= 0.4m f
Future Prospect: Fully Covariant Basis Light-Front Quantization (BLFQ) Example: Positronium in QED at strong coupling
P. Wiecki, Y. Li, X. Zhao, P. Maris and J.P. Vary, arXiv 1404.6234
X Pert. theory at α4
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Conclusions/Outlook # Impressive recent progress in deriving NN and NNN interac'ons from QCD
# Much work needs to be done to improve upon these interac'ons and the many-‐body approaches that employ them
# We will con'nue to apply these interac'ons to nuclei as they are developed # Collabora'ons of Chiral EFT theorists and ab-‐ini'o many-‐body theorists underway
to improve the proper'es of the Chiral EFT interac'ons
# Collabora'ons of nuclear theorists with computer scien'sts and applied mathema'cians must con'nue
# Increasing computa'onal resources needed (3NFs, 4NFs are major challenges)
# Increased manpower needed to achieve these goals in larger collabora'ng teams
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Recent Collaborators United States ISU: Pieter Maris, George Papadimitriou, Chase Cockrell, Hugh Potter, Alina Negoita LLNL: Erich Ormand, Tom Luu, Eric Jurgenson, Michael Kruse ORNL/UT: David Dean, Hai Ah Nam, Markus Kortelainen, Witek Nazarewicz, Gaute Hagen,Thomas Papenbrock OSU: Dick Furnstahl, students MSU: Scott Bogner, Heiko Hergert Notre Dame: Mark Caprio ANL: Harry Lee, Steve Pieper, Fritz Coester LANL: Joe Carlson, Stefano Gandolfi UA: Bruce Barrett, Sid A. Coon, Bira van Kolck, Matthew Avetian, Alexander Lisetskiy LSU: Jerry Draayer, Tomas Dytrych, Kristina Sviratcheva, Chairul Bahri UW: Martin Savage
International Canada: Petr Navratil Russia: Andrey Shirokov, Alexander Mazur, Eugene Mazur, Sergey Zaytsev, Vasily Kulikov Sweden: Christian Forssen, Jimmy Rotureau Japan: Takashi Abe, Takaharu Otsuka, Yutaka Utsuno, Noritaka Shimizu Germany: Achim Schwenk, Robert Roth, Kai Hebeler, students South Korea: Youngman Kim, Ik Jae Shin Turkey: Erdal Dikman
ODU/Ames Lab: Masha Sosonkina, Dossay Oryspayev LBNL: Esmond Ng, Chao Yang, Hasan Metin Aktulga ANL: Stefan Wild, Rusty Lusk OSU: Umit Catalyurek, Eric Saule
Quantum Field
Theory
ISU: Xingbo Zhao, Pieter Maris, Germany: Hans-Juergen Pirner Paul Wiecki, Yang Li, Kirill Tuchin, Costa Rica: Guy de Teramond John Spence India: Avaroth Harindranath, Stanford: Stan Brodsky Usha Kulshreshtha, Daya Kulshreshtha, Penn State: Heli Honkanen Asmita Mukherjee, Dipankar Chakrabarti, Russia: Vladimir Karmanov Ravi Manohar
Computer Science/ Applied Math